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- La ecuación:
-
Ecuación x/4+13=x+1
-
Ecuación 0,2x+2,7=1,4-1,1x
-
Ecuación 2x^2-x-1=x^2-5x-(-1-x^2)
-
Ecuación 5(x-2)^2=-6x-44
- Expresar {x} en función de y en la ecuación:
- -2*x+14*y=9
- -6*x-20*y=8
- 2*x-8*y=4
- -9*x-1*y=6
- Integral de d{x}:
- sin3xsin5x
-
Expresiones idénticas
- cos4xcos2x=sin3xsin5x
- coseno de 4x coseno de 2x es igual a seno de 3x seno de 5x
-
Expresiones semejantes
- √3(cos4x+1)=2(2-cos4x)cos2x
- 8*cos(4*x)*cos(2*x)*cos(3*x)=1
cos4xcos2x=sin3xsin5x la ecuación
El profesor se sorprenderá mucho al ver tu solución correcta😉
Solución
Ha introducido
[src]
cos(4*x)*cos(2*x) = sin(3*x)*sin(5*x)
$$\cos{\left(2 x \right)} \cos{\left(4 x \right)} = \sin{\left(3 x \right)} \sin{\left(5 x \right)}$$
Suma y producto de raíces
[src]
suma
/ /pi\\ / /pi\\ / /pi\\ / /pi\\
/ _____________________\ |cos|--|| |cos|--|| / _____________________\ |cos|--|| / _____________________\ / _____________________\ |cos|--||
pi 3*pi pi pi 3*pi pi 11*pi 13*pi / 14____\ / 3/14\ | / 2/pi\ 2/pi\ | | \7 /| | \7 /| | / 2/pi\ 2/pi\ | | \7 /| | / 2/pi\ 2/pi\ | | / 2/pi\ 2/pi\ | | \7 /|
- -- - ---- - -- + -- + ---- + -- + ----- + ----- - I*log\-\/ -1 / - I*log\-(-1) / + -pi - I*log| / cos |--| + sin |--| | + atan|-------| + pi - atan|-------| - I*log| / cos |--| + sin |--| | + - atan|-------| - I*log| / cos |--| + sin |--| | + - I*log| / cos |--| + sin |--| | + atan|-------|
2 14 14 14 14 2 14 14 \\/ \7 / \7 / / | /pi\| | /pi\| \\/ \7 / \7 / / | /pi\| \\/ \7 / \7 / / \\/ \7 / \7 / / | /pi\|
|sin|--|| |sin|--|| |sin|--|| |sin|--||
\ \7 // \ \7 // \ \7 // \ \7 //
$$\left(\left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)}\right) + \left(\left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \pi\right) + \left(\left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right) + \left(- i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)} + \left(- i \log{\left(- \sqrt[14]{-1} \right)} + \left(\left(\left(\left(\left(\left(\left(- \frac{\pi}{2} - \frac{3 \pi}{14}\right) - \frac{\pi}{14}\right) + \frac{\pi}{14}\right) + \frac{3 \pi}{14}\right) + \frac{\pi}{2}\right) + \frac{11 \pi}{14}\right) + \frac{13 \pi}{14}\right)\right)\right)\right)\right)\right) + \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right)$$
=
/ _____________________\ 12*pi / 14____\ / 3/14\ | / 2/pi\ 2/pi\ | ----- - I*log\-\/ -1 / - I*log\-(-1) / - 4*I*log| / cos |--| + sin |--| | 7 \\/ \7 / \7 / /
$$- i \log{\left(- \sqrt[14]{-1} \right)} - i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)} - 4 i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \frac{12 \pi}{7}$$
producto
/ / /pi\\\ / / /pi\\ \ / / /pi\\ \ / / /pi\\\
| / _____________________\ |cos|--||| | |cos|--|| / _____________________\| | |cos|--|| / _____________________\| | / _____________________\ |cos|--|||
-pi -3*pi -pi pi 3*pi pi 11*pi 13*pi / / 14____\\ / / 3/14\\ | | / 2/pi\ 2/pi\ | | \7 /|| | | \7 /| | / 2/pi\ 2/pi\ || | | \7 /| | / 2/pi\ 2/pi\ || | | / 2/pi\ 2/pi\ | | \7 /||
----*-----*----*--*----*--*-----*-----*\-I*log\-\/ -1 //*\-I*log\-(-1) //*|-pi - I*log| / cos |--| + sin |--| | + atan|-------||*|pi - atan|-------| - I*log| / cos |--| + sin |--| ||*|- atan|-------| - I*log| / cos |--| + sin |--| ||*|- I*log| / cos |--| + sin |--| | + atan|-------||
2 14 14 14 14 2 14 14 | \\/ \7 / \7 / / | /pi\|| | | /pi\| \\/ \7 / \7 / /| | | /pi\| \\/ \7 / \7 / /| | \\/ \7 / \7 / / | /pi\||
| |sin|--||| | |sin|--|| | | |sin|--|| | | |sin|--|||
\ \ \7 /// \ \ \7 // / \ \ \7 // / \ \ \7 ///
$$- i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)} - i \log{\left(- \sqrt[14]{-1} \right)} \frac{13 \pi}{14} \frac{11 \pi}{14} \frac{\pi}{2} \frac{3 \pi}{14} \frac{\pi}{14} \cdot - \frac{\pi}{14} \cdot - \frac{\pi}{2} \left(- \frac{3 \pi}{14}\right) \left(- \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \pi\right) \left(- \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)}\right) \left(- i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}\right)$$
=
12 / 14____\ / 3/14\
2606175*pi *log\-\/ -1 /*log\-(-1) /
----------------------------------------
1157018619904
$$\frac{2606175 \pi^{12} \log{\left(- \sqrt[14]{-1} \right)} \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)}}{1157018619904}$$
2606175*pi^12*log(-(-1)^(1/14))*log(-(-1)^(3/14))/1157018619904
Respuesta rápida
[src]
-pi
x1 = ----
2
$$x_{1} = - \frac{\pi}{2}$$
-3*pi
x2 = -----
14
$$x_{2} = - \frac{3 \pi}{14}$$
-pi
x3 = ----
14
$$x_{3} = - \frac{\pi}{14}$$
pi
x4 = --
14
$$x_{4} = \frac{\pi}{14}$$
3*pi
x5 = ----
14
$$x_{5} = \frac{3 \pi}{14}$$
pi
x6 = --
2
$$x_{6} = \frac{\pi}{2}$$
11*pi
x7 = -----
14
$$x_{7} = \frac{11 \pi}{14}$$
13*pi
x8 = -----
14
$$x_{8} = \frac{13 \pi}{14}$$
/ 14____\ x9 = -I*log\-\/ -1 /
$$x_{9} = - i \log{\left(- \sqrt[14]{-1} \right)}$$
/ 3/14\ x10 = -I*log\-(-1) /
$$x_{10} = - i \log{\left(- \left(-1\right)^{\frac{3}{14}} \right)}$$
/ /pi\\
/ _____________________\ |cos|--||
| / 2/pi\ 2/pi\ | | \7 /|
x11 = -pi - I*log| / cos |--| + sin |--| | + atan|-------|
\\/ \7 / \7 / / | /pi\|
|sin|--||
\ \7 //
$$x_{11} = - \pi - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}$$
/ /pi\\
|cos|--|| / _____________________\
| \7 /| | / 2/pi\ 2/pi\ |
x12 = pi - atan|-------| - I*log| / cos |--| + sin |--| |
| /pi\| \\/ \7 / \7 / /
|sin|--||
\ \7 //
$$x_{12} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \pi$$
/ /pi\\
|cos|--|| / _____________________\
| \7 /| | / 2/pi\ 2/pi\ |
x13 = - atan|-------| - I*log| / cos |--| + sin |--| |
| /pi\| \\/ \7 / \7 / /
|sin|--||
\ \7 //
$$x_{13} = - \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)} - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)}$$
/ /pi\\
/ _____________________\ |cos|--||
| / 2/pi\ 2/pi\ | | \7 /|
x14 = - I*log| / cos |--| + sin |--| | + atan|-------|
\\/ \7 / \7 / / | /pi\|
|sin|--||
\ \7 //
$$x_{14} = - i \log{\left(\sqrt{\sin^{2}{\left(\frac{\pi}{7} \right)} + \cos^{2}{\left(\frac{\pi}{7} \right)}} \right)} + \operatorname{atan}{\left(\frac{\cos{\left(\frac{\pi}{7} \right)}}{\sin{\left(\frac{\pi}{7} \right)}} \right)}$$
x14 = -i*log(sqrt(sin(pi/7)^2 + cos(pi/7)^2)) + atan(cos(pi/7)/sin(pi/7))
Respuesta numérica
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x1 = -7.85398156908478
x2 = 84.1498032211552
x3 = -72.0322315573088
x4 = -55.875469338847
x5 = 18.1763574957695
x6 = 46.0018924275648
x7 = -81.905808468591
x8 = 14.1371666781978
x9 = -80.1106127288493
x10 = -39.7187071203852
x11 = -37.9235113183339
x12 = -29.8451301480097
x13 = -67.9930410026934
x14 = 86.3937983040671
x15 = 40.1675060708981
x16 = -25.8059396544876
x17 = -19.9715532978208
x18 = -61.7098556955138
x19 = 32.0891249616672
x20 = -73.8274272888222
x21 = -98.0625706870528
x22 = 74.276226309873
x23 = 54.0802735367957
x24 = 0.224399475256414
x25 = 2.01959527730772
x26 = -3.81479107935903
x27 = 64.4026491723469
x28 = -54.5290724873086
x29 = 50.0410829821803
x30 = 10.0979763865386
x31 = 42.4115010150339
x32 = 52.7338766852572
x33 = -33.8843207637185
x34 = 88.1889937757706
x35 = 58.1194639733282
x36 = -76.0714221119243
x37 = -10.9955743995035
x38 = -21.7667490998721
x39 = -83.7010042706423
x40 = 4.26359002987186
x41 = 96.2673748850015
x42 = 92.6769831195842
x43 = 19.9715532978208
x44 = 94.0233801324374
x45 = -32.9867228544314
x46 = 67.9930410026934
x47 = 24.0107438524363
x48 = 388.884290619365
x49 = -69.7882368047447
x50 = -91.7793853798732
x51 = 6.05878583192317
x52 = 80.1106126783847
x53 = -51.8362787100334
x54 = -15.9323627432054
x55 = 62.1586546460266
x56 = 66.1978452006421
x57 = -11.8931721885899
x58 = -50.0410829821803
x59 = -46.0018924275648
x60 = -6.05878583192317
x61 = -63.9538504480779
x62 = 70.2370357552575
x63 = 89.9841895778219
x64 = 98.0625706870528
x65 = 35.6795165657698
x66 = -58.1194641568646
x67 = 92.2281843303861
x68 = 22.215548050385
x69 = -28.0499344070517
x70 = -47.7970882296161
x71 = 48.245887180129
x72 = -41.9627018729494
x73 = -43.7578976750007
x74 = -5.60998688141034
x75 = -17.7275585452567
x76 = 54.9778717349604
x77 = -89.9841895778219
x78 = 76.0714221119243
x79 = -24.0107438524363
x80 = 72.0322315573088
x81 = 26.2547386050004
x82 = -65.7490462501292
x83 = -87.7401948252578
x84 = -77.8666179139756
x85 = -94.0233801324374
x86 = -59.9146598934625
x87 = 58.1194639815683
x88 = 28.0499344070517
x89 = 100.306565439617
x90 = -85.9449990232065
x91 = -95.8185758715514
x92 = -2.01959527730772
x93 = -99.8577664891041
x94 = 44.2066966255135
x94 = 44.2066966255135